LMFDB - Embedded newform 1096.1.z.a.443.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1096,1,Mod(11,1096)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1096, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([34, 34, 61]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1096.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1096 = 2^{3} \cdot 137 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1096.z (of order $68$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.546975253846$
Analytic rank:	$0$
Dimension:	$32$
Coefficient field:	$\Q(\zeta_{68})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \cdots + 1 $ x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{68}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{68} - \cdots)$

Embedding invariants

Embedding label			443.1
Root			$-0.798017 - 0.602635i$ of defining polynomial
Character	$\chi$	$=$	1096.443
Dual form			1096.1.z.a.715.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.526432 + 0.850217i) q^{2} +(-0.516087 - 1.16883i) q^{3} +(-0.445738 - 0.895163i) q^{4} +(1.26544 + 0.176521i) q^{6} +(0.995734 + 0.0922684i) q^{8} +(-0.426113 + 0.467424i) q^{9} +O(q^{10})$	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.516087 - 1.16883i) q^{3} +(-0.445738 - 0.895163i) q^{4} +(1.26544 + 0.176521i) q^{6} +(0.995734 + 0.0922684i) q^{8} +(-0.426113 + 0.467424i) q^{9} +(1.07891 - 0.537235i) q^{11} +(-0.816250 + 0.982973i) q^{12} +(-0.602635 + 0.798017i) q^{16} +(-1.58923 + 0.147263i) q^{17} +(-0.173092 - 0.608356i) q^{18} +(1.91545 - 0.544991i) q^{19} +(-0.111208 + 1.20013i) q^{22} +(-0.406040 - 1.21146i) q^{24} +(-0.895163 - 0.445738i) q^{25} +(-0.445210 - 0.149219i) q^{27} +(-0.361242 - 0.932472i) q^{32} +(-1.18475 - 0.983802i) q^{33} +(0.711414 - 1.42871i) q^{34} +(0.608356 + 0.173092i) q^{36} +(-0.544991 + 1.91545i) q^{38} +(0.571231 - 0.571231i) q^{41} +(0.963876 - 1.73049i) q^{43} +(-0.961826 - 0.726337i) q^{44} +(1.24376 + 0.292529i) q^{48} +(-0.932472 + 0.361242i) q^{49} +(0.850217 - 0.526432i) q^{50} +(0.992305 + 1.78153i) q^{51} +(0.361242 - 0.299971i) q^{54} +(-1.62554 - 1.95756i) q^{57} +(-1.25664 - 1.14558i) q^{59} +(0.982973 + 0.183750i) q^{64} +(1.46013 - 0.489388i) q^{66} +(0.869557 - 1.26940i) q^{67} +(0.840204 + 1.35698i) q^{68} +(-0.467424 + 0.426113i) q^{72} +(0.710182 + 0.132756i) q^{73} +(-0.0590083 + 1.27633i) q^{75} +(-1.34164 - 1.47171i) q^{76} +(0.113716 + 1.22719i) q^{81} +(0.184956 + 0.786384i) q^{82} +(-1.26940 + 1.05409i) q^{83} +(0.963876 + 1.73049i) q^{86} +(1.12388 - 0.435393i) q^{88} +(0.947359 + 0.222817i) q^{89} +(-0.903466 + 0.903466i) q^{96} +(-0.201983 + 0.602635i) q^{97} +(0.183750 - 0.982973i) q^{98} +(-0.208623 + 0.733232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	$ 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times$.

$n$	$549$	$823$	$825$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{25}{68}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$2$	−0.526432	+	0.850217i	−0.526432	+	0.850217i
$3$	−0.516087	−	1.16883i	−0.516087	−	1.16883i	−0.961826	−	0.273663i	$-0.911765\pi$
$3$	−0.516087	−	1.16883i	−0.516087	−	1.16883i	0.445738	−	0.895163i	$-0.352941\pi$
$4$	−0.445738	−	0.895163i	−0.445738	−	0.895163i
$5$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$5$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$6$	1.26544	+	0.176521i	1.26544	+	0.176521i
$7$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$7$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$8$	0.995734	+	0.0922684i	0.995734	+	0.0922684i
$9$	−0.426113	+	0.467424i	−0.426113	+	0.467424i
$10$		0			0
$11$	1.07891	−	0.537235i	1.07891	−	0.537235i	0.183750	−	0.982973i	$-0.441176\pi$
$11$	1.07891	−	0.537235i	1.07891	−	0.537235i	0.895163	+	0.445738i	$0.147059\pi$
$12$	−0.816250	+	0.982973i	−0.816250	+	0.982973i
$13$		0			0		−0.824997	−	0.565136i	$-0.808824\pi$
$13$		0			0		0.824997	+	0.565136i	$0.191176\pi$
$14$		0			0
$15$		0			0
$16$	−0.602635	+	0.798017i	−0.602635	+	0.798017i
$17$	−1.58923	+	0.147263i	−1.58923	+	0.147263i	−0.850217	−	0.526432i	$-0.823529\pi$
$17$	−1.58923	+	0.147263i	−1.58923	+	0.147263i	−0.739009	+	0.673696i	$0.764706\pi$
$18$	−0.173092	−	0.608356i	−0.173092	−	0.608356i
$19$	1.91545	−	0.544991i	1.91545	−	0.544991i	0.932472	−	0.361242i	$-0.117647\pi$
$19$	1.91545	−	0.544991i	1.91545	−	0.544991i	0.982973	−	0.183750i	$-0.0588235\pi$
$20$		0			0
$21$		0			0
$22$	−0.111208	+	1.20013i	−0.111208	+	1.20013i
$23$		0			0		0.990410	−	0.138156i	$-0.0441176\pi$
$23$		0			0		−0.990410	+	0.138156i	$0.955882\pi$
$24$	−0.406040	−	1.21146i	−0.406040	−	1.21146i
$25$	−0.895163	−	0.445738i	−0.895163	−	0.445738i
$26$		0			0
$27$	−0.445210	−	0.149219i	−0.445210	−	0.149219i
$28$		0			0
$29$		0			0		−0.138156	−	0.990410i	$-0.544118\pi$
$29$		0			0		0.138156	+	0.990410i	$0.455882\pi$
$30$		0			0
$31$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$31$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$32$	−0.361242	−	0.932472i	−0.361242	−	0.932472i
$33$	−1.18475	−	0.983802i	−1.18475	−	0.983802i
$34$	0.711414	−	1.42871i	0.711414	−	1.42871i
$35$		0			0
$36$	0.608356	+	0.173092i	0.608356	+	0.173092i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	−0.544991	+	1.91545i	−0.544991	+	1.91545i
$39$		0			0
$40$		0			0
$41$	0.571231	−	0.571231i	0.571231	−	0.571231i	−0.361242	−	0.932472i	$-0.617647\pi$
$41$	0.571231	−	0.571231i	0.571231	−	0.571231i	0.932472	+	0.361242i	$0.117647\pi$
$42$		0			0
$43$	0.963876	−	1.73049i	0.963876	−	1.73049i	0.361242	−	0.932472i	$-0.382353\pi$
$43$	0.963876	−	1.73049i	0.963876	−	1.73049i	0.602635	−	0.798017i	$-0.294118\pi$
$44$	−0.961826	−	0.726337i	−0.961826	−	0.726337i
$45$		0			0
$46$		0			0
$47$		0			0		0.998933	−	0.0461835i	$-0.0147059\pi$
$47$		0			0		−0.998933	+	0.0461835i	$0.985294\pi$
$48$	1.24376	+	0.292529i	1.24376	+	0.292529i
$49$	−0.932472	+	0.361242i	−0.932472	+	0.361242i
$50$	0.850217	−	0.526432i	0.850217	−	0.526432i
$51$	0.992305	+	1.78153i	0.992305	+	1.78153i
$52$		0			0
$53$		0			0		−0.873622	−	0.486604i	$-0.838235\pi$
$53$		0			0		0.873622	+	0.486604i	$0.161765\pi$
$54$	0.361242	−	0.299971i	0.361242	−	0.299971i
$55$		0			0
$56$		0			0
$57$	−1.62554	−	1.95756i	−1.62554	−	1.95756i
$58$		0			0
$59$	−1.25664	−	1.14558i	−1.25664	−	1.14558i	−0.982973	−	0.183750i	$-0.941176\pi$
$59$	−1.25664	−	1.14558i	−1.25664	−	1.14558i	−0.273663	−	0.961826i	$-0.588235\pi$
$60$		0			0
$61$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$61$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$62$		0			0
$63$		0			0
$64$	0.982973	+	0.183750i	0.982973	+	0.183750i
$65$		0			0
$66$	1.46013	−	0.489388i	1.46013	−	0.489388i
$67$	0.869557	−	1.26940i	0.869557	−	1.26940i	−0.0922684	−	0.995734i	$-0.529412\pi$
$67$	0.869557	−	1.26940i	0.869557	−	1.26940i	0.961826	−	0.273663i	$-0.0882353\pi$
$68$	0.840204	+	1.35698i	0.840204	+	1.35698i
$69$		0			0
$70$		0			0
$71$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$71$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$72$	−0.467424	+	0.426113i	−0.467424	+	0.426113i
$73$	0.710182	+	0.132756i	0.710182	+	0.132756i	0.526432	−	0.850217i	$-0.323529\pi$
$73$	0.710182	+	0.132756i	0.710182	+	0.132756i	0.183750	+	0.982973i	$0.441176\pi$
$74$		0			0
$75$	−0.0590083	+	1.27633i	−0.0590083	+	1.27633i
$76$	−1.34164	−	1.47171i	−1.34164	−	1.47171i
$77$		0			0
$78$		0			0
$79$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$79$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$80$		0			0
$81$	0.113716	+	1.22719i	0.113716	+	1.22719i
$82$	0.184956	+	0.786384i	0.184956	+	0.786384i
$83$	−1.26940	+	1.05409i	−1.26940	+	1.05409i	−0.273663	+	0.961826i	$0.588235\pi$
$83$	−1.26940	+	1.05409i	−1.26940	+	1.05409i	−0.995734	+	0.0922684i	$0.970588\pi$
$84$		0			0
$85$		0			0
$86$	0.963876	+	1.73049i	0.963876	+	1.73049i
$87$		0			0
$88$	1.12388	−	0.435393i	1.12388	−	0.435393i
$89$	0.947359	+	0.222817i	0.947359	+	0.222817i	0.673696	−	0.739009i	$-0.264706\pi$
$89$	0.947359	+	0.222817i	0.947359	+	0.222817i	0.273663	+	0.961826i	$0.411765\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.903466	+	0.903466i	−0.903466	+	0.903466i
$97$	−0.201983	+	0.602635i	−0.201983	+	0.602635i	0.798017	+	0.602635i	$0.205882\pi$
$97$	−0.201983	+	0.602635i	−0.201983	+	0.602635i	−1.00000			$\pi$
$98$	0.183750	−	0.982973i	0.183750	−	0.982973i
$99$	−0.208623	+	0.733232i	−0.208623	+	0.733232i
$100$			1.00000i			1.00000i
$101$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$101$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$102$	−2.03707	−	0.0941793i	−2.03707	−	0.0941793i
$103$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$103$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.710182	+	1.83319i	−0.710182	+	1.83319i	−0.183750	+	0.982973i	$0.558824\pi$
$107$	−0.710182	+	1.83319i	−0.710182	+	1.83319i	−0.526432	+	0.850217i	$0.676471\pi$
$108$	0.0648715	+	0.465048i	0.0648715	+	0.465048i
$109$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$109$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.581427	+	1.73474i	0.581427	+	1.73474i	0.673696	+	0.739009i	$0.264706\pi$
$113$	0.581427	+	1.73474i	0.581427	+	1.73474i	−0.0922684	+	0.995734i	$0.529412\pi$
$114$	2.52009	−	0.351537i	2.52009	−	0.351537i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.63552	−	0.465346i	1.63552	−	0.465346i
$119$		0			0
$120$		0			0
$121$	0.272797	−	0.361242i	0.272797	−	0.361242i
$122$		0			0
$123$	−0.962474	−	0.372864i	−0.962474	−	0.372864i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$127$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$128$	−0.673696	+	0.739009i	−0.673696	+	0.739009i
$129$	−2.52009	−	0.233520i	−2.52009	−	0.233520i
$130$		0			0
$131$	0.273663	+	0.0381744i	0.273663	+	0.0381744i	0.273663	−	0.961826i	$-0.411765\pi$
$131$	0.273663	+	0.0381744i	0.273663	+	0.0381744i			1.00000i	$0.5\pi$
$132$	−0.352576	+	1.49906i	−0.352576	+	1.49906i
$133$		0			0
$134$	0.621500	+	1.40756i	0.621500	+	1.40756i
$135$		0			0
$136$	−1.59603			−1.59603
$137$	0.961826	+	0.273663i	0.961826	+	0.273663i
$137$	0.961826	+	0.273663i	0.961826	+	0.273663i
$138$		0			0
$139$	−0.0971461	+	0.156896i	−0.0971461	+	0.156896i	−0.895163	−	0.445738i	$-0.852941\pi$
$139$	−0.0971461	+	0.156896i	−0.0971461	+	0.156896i	0.798017	+	0.602635i	$0.205882\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.116222	−	0.621731i	−0.116222	−	0.621731i
$145$		0			0
$146$	−0.486734	+	0.533922i	−0.486734	+	0.533922i
$147$	0.903466	+	0.903466i	0.903466	+	0.903466i
$148$		0			0
$149$		0			0		0.638847	−	0.769334i	$-0.279412\pi$
$149$		0			0		−0.638847	+	0.769334i	$0.720588\pi$
$150$	−1.05409	−	0.722071i	−1.05409	−	0.722071i
$151$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$151$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$152$	1.95756	−	0.365931i	1.95756	−	0.365931i
$153$	0.608356	−	0.805593i	0.608356	−	0.805593i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$157$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.10324	−	0.549347i	−1.10324	−	0.549347i
$163$	1.73474	−	0.765964i	1.73474	−	0.765964i	0.739009	−	0.673696i	$-0.235294\pi$
$163$	1.73474	−	0.765964i	1.73474	−	0.765964i	0.995734	−	0.0922684i	$-0.0294118\pi$
$164$	−0.765964	−	0.256725i	−0.765964	−	0.256725i
$165$		0			0
$166$	−0.227957	−	1.63417i	−0.227957	−	1.63417i
$167$		0			0		0.361242	−	0.932472i	$-0.382353\pi$
$167$		0			0		−0.361242	+	0.932472i	$0.617647\pi$
$168$		0			0
$169$	0.361242	+	0.932472i	0.361242	+	0.932472i
$170$		0			0
$171$	−0.561455	+	1.12755i	−0.561455	+	1.12755i
$172$	−1.97871	−	0.0914812i	−1.97871	−	0.0914812i
$173$		0			0		−0.961826	−	0.273663i	$-0.911765\pi$
$173$		0			0		0.961826	+	0.273663i	$0.0882353\pi$
$174$		0			0
$175$		0			0
$176$	−0.221468	+	1.18475i	−0.221468	+	1.18475i
$177$	−0.690444	+	2.06001i	−0.690444	+	2.06001i
$178$	−0.688163	+	0.688163i	−0.688163	+	0.688163i
$179$	0.0844967	+	1.82764i	0.0844967	+	1.82764i	0.445738	+	0.895163i	$0.352941\pi$
$179$	0.0844967	+	1.82764i	0.0844967	+	1.82764i	−0.361242	+	0.932472i	$0.617647\pi$
$180$		0			0
$181$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$181$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.63552	+	1.01267i	−1.63552	+	1.01267i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$191$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$192$	−0.292529	−	1.24376i	−0.292529	−	1.24376i
$193$	−0.165190	−	1.78269i	−0.165190	−	1.78269i	−0.526432	−	0.850217i	$-0.676471\pi$
$193$	−0.165190	−	1.78269i	−0.165190	−	1.78269i	0.361242	−	0.932472i	$-0.382353\pi$
$194$	−0.406040	−	0.488975i	−0.406040	−	0.488975i
$195$		0			0
$196$	0.739009	+	0.673696i	0.739009	+	0.673696i
$197$		0			0		−0.602635	−	0.798017i	$-0.705882\pi$
$197$		0			0		0.602635	+	0.798017i	$0.294118\pi$
$198$	−0.513581	−	0.563372i	−0.513581	−	0.563372i
$199$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$199$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$200$	−0.850217	−	0.526432i	−0.850217	−	0.526432i
$201$	−1.93247	−	0.361242i	−1.93247	−	0.361242i
$202$		0			0
$203$		0			0
$204$	1.15245	−	1.68237i	1.15245	−	1.68237i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.77381	−	1.61704i	1.77381	−	1.61704i
$210$		0			0
$211$	−0.895163	−	0.554262i	−0.895163	−	0.554262i		−	1.00000i	$-0.5\pi$
$211$	−0.895163	−	0.554262i	−0.895163	−	0.554262i	−0.895163	+	0.445738i	$0.852941\pi$
$212$		0			0
$213$		0			0
$214$	−1.18475	−	1.56886i	−1.18475	−	1.56886i
$215$		0			0
$216$	−0.429543	−	0.189662i	−0.429543	−	0.189662i
$217$		0			0
$218$		0			0
$219$	−0.211347	−	0.898593i	−0.211347	−	0.898593i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$223$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$224$		0			0
$225$	0.589790	−	0.228486i	0.589790	−	0.228486i
$226$	−1.78099	−	0.418885i	−1.78099	−	0.418885i
$227$	1.64823	−	0.0762025i	1.64823	−	0.0762025i	0.798017	−	0.602635i	$-0.205882\pi$
$227$	1.64823	−	0.0762025i	1.64823	−	0.0762025i	0.850217	+	0.526432i	$0.176471\pi$
$228$	−1.02777	+	2.32768i	−1.02777	+	2.32768i
$229$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$229$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.34090	−	1.34090i	1.34090	−	1.34090i	0.445738	−	0.895163i	$-0.352941\pi$
$233$	1.34090	−	1.34090i	1.34090	−	1.34090i	0.895163	−	0.445738i	$-0.147059\pi$
$234$		0			0
$235$		0			0
$236$	−0.465346	+	1.63552i	−0.465346	+	1.63552i
$237$		0			0
$238$		0			0
$239$		0			0		−0.998933	−	0.0461835i	$-0.985294\pi$
$239$		0			0		0.998933	+	0.0461835i	$0.0147059\pi$
$240$		0			0
$241$	0.488975	+	0.406040i	0.488975	+	0.406040i	0.850217	−	0.526432i	$-0.176471\pi$
$241$	0.488975	+	0.406040i	0.488975	+	0.406040i	−0.361242	+	0.932472i	$0.617647\pi$
$242$	0.163525	+	0.422106i	0.163525	+	0.422106i
$243$	0.965470	−	0.537763i	0.965470	−	0.537763i
$244$		0			0
$245$		0			0
$246$	0.823693	−	0.622024i	0.823693	−	0.622024i
$247$		0			0
$248$		0			0
$249$	1.88717	+	0.939700i	1.88717	+	0.939700i
$250$		0			0
$251$	−0.273663	+	0.0381744i	−0.273663	+	0.0381744i	−0.273663	−	0.961826i	$-0.588235\pi$
$251$	−0.273663	+	0.0381744i	−0.273663	+	0.0381744i			1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.273663	−	0.961826i	−0.273663	−	0.961826i
$257$	−1.85699	+	0.172075i	−1.85699	+	0.172075i	−0.961826	−	0.273663i	$-0.911765\pi$
$257$	−1.85699	+	0.172075i	−1.85699	+	0.172075i	−0.895163	+	0.445738i	$0.852941\pi$
$258$	1.52520	−	2.01969i	1.52520	−	2.01969i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.176521	+	0.212577i	−0.176521	+	0.212577i
$263$		0			0		0.895163	−	0.445738i	$-0.147059\pi$
$263$		0			0		−0.895163	+	0.445738i	$0.852941\pi$
$264$	−1.08892	−	1.08892i	−1.08892	−	1.08892i
$265$		0			0
$266$		0			0
$267$	−0.228486	−	1.22229i	−0.228486	−	1.22229i
$268$	−1.52391	−	0.212577i	−1.52391	−	0.212577i
$269$		0			0		0.228951	−	0.973438i	$-0.426471\pi$
$269$		0			0		−0.228951	+	0.973438i	$0.573529\pi$
$270$		0			0
$271$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$271$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$272$	0.840204	−	1.35698i	0.840204	−	1.35698i
$273$		0			0
$274$	−0.739009	+	0.673696i	−0.739009	+	0.673696i
$275$	−1.20527			−1.20527
$276$		0			0
$277$		0			0		−0.403921	−	0.914794i	$-0.632353\pi$
$277$		0			0		0.403921	+	0.914794i	$0.367647\pi$
$278$	−0.0822551	−	0.165190i	−0.0822551	−	0.165190i
$279$		0			0
$280$		0			0
$281$	0.0339085	+	0.181395i	0.0339085	+	0.181395i	0.995734	−	0.0922684i	$-0.0294118\pi$
$281$	0.0339085	+	0.181395i	0.0339085	+	0.181395i	−0.961826	+	0.273663i	$0.911765\pi$
$282$		0			0
$283$	−0.907732	+	0.995734i	−0.907732	+	0.995734i	0.0922684	+	0.995734i	$0.470588\pi$
$283$	−0.907732	+	0.995734i	−0.907732	+	0.995734i	−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.589790	+	0.228486i	0.589790	+	0.228486i
$289$	1.52098	−	0.284320i	1.52098	−	0.284320i
$290$		0			0
$291$	0.808616	−	0.0749293i	0.808616	−	0.0749293i
$292$	−0.197717	−	0.694903i	−0.197717	−	0.694903i
$293$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$293$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$294$	−1.24376	+	0.292529i	−1.24376	+	0.292529i
$295$		0			0
$296$		0			0
$297$	−0.560509	+	0.0781876i	−0.560509	+	0.0781876i
$298$		0			0
$299$		0			0
$300$	1.16883	−	0.516087i	1.16883	−	0.516087i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.719401	+	1.85699i	−0.719401	+	1.85699i
$305$		0			0
$306$	0.364671	+	0.941324i	0.364671	+	0.941324i
$307$	1.18375	+	0.982973i	1.18375	+	0.982973i	1.00000			$0$
$307$	1.18375	+	0.982973i	1.18375	+	0.982973i	0.183750	+	0.982973i	$0.441176\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−0.353470	+	1.89090i	−0.353470	+	1.89090i	0.0922684	+	0.995734i	$0.470588\pi$
$313$	−0.353470	+	1.89090i	−0.353470	+	1.89090i	−0.445738	+	0.895163i	$0.647059\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.486604	−	0.873622i	$-0.338235\pi$
$317$		0			0		−0.486604	+	0.873622i	$0.661765\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.50920	−	0.116007i	2.50920	−	0.116007i
$322$		0			0
$323$	−2.96382	+	1.14819i	−2.96382	+	1.14819i
$324$	1.04784	−	0.648798i	1.04784	−	0.648798i
$325$		0			0
$326$	−0.261989	+	1.87814i	−0.261989	+	1.87814i
$327$		0			0
$328$	0.621500	−	0.516087i	0.621500	−	0.516087i
$329$		0			0
$330$		0			0
$331$	0.903466	+	1.08800i	0.903466	+	1.08800i	0.995734	+	0.0922684i	$0.0294118\pi$
$331$	0.903466	+	1.08800i	0.903466	+	1.08800i	−0.0922684	+	0.995734i	$0.529412\pi$
$332$	1.50941	+	0.666468i	1.50941	+	0.666468i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.614268	+	0.380338i	0.614268	+	0.380338i	0.798017	−	0.602635i	$-0.205882\pi$
$337$	0.614268	+	0.380338i	0.614268	+	0.380338i	−0.183750	+	0.982973i	$0.558824\pi$
$338$	−0.982973	−	0.183750i	−0.982973	−	0.183750i
$339$	1.72755	−	1.57487i	1.72755	−	1.57487i
$340$		0			0
$341$		0			0
$342$	−0.663097	−	1.07094i	−0.663097	−	1.07094i
$343$		0			0
$344$	1.11943	−	1.63417i	1.11943	−	1.63417i
$345$		0			0
$346$		0			0
$347$	1.45285	+	0.271585i	1.45285	+	0.271585i	0.850217	−	0.526432i	$-0.176471\pi$
$347$	1.45285	+	0.271585i	1.45285	+	0.271585i	0.602635	+	0.798017i	$0.294118\pi$
$348$		0			0
$349$		0			0		0.0461835	−	0.998933i	$-0.485294\pi$
$349$		0			0		−0.0461835	+	0.998933i	$0.514706\pi$
$350$		0			0
$351$		0			0
$352$	−0.890705	−	0.811985i	−0.890705	−	0.811985i
$353$	−1.03397	−	0.456541i	−1.03397	−	0.456541i	−0.183750	−	0.982973i	$-0.558824\pi$
$353$	−1.03397	−	0.456541i	−1.03397	−	0.456541i	−0.850217	+	0.526432i	$0.823529\pi$
$354$	−1.38798	−	1.67148i	−1.38798	−	1.67148i
$355$		0			0
$356$	−0.222817	−	0.947359i	−0.222817	−	0.947359i
$357$		0			0
$358$	−1.59837	−	0.890286i	−1.59837	−	0.890286i
$359$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$359$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$360$		0			0
$361$	2.52170	−	1.56137i	2.52170	−	1.56137i
$362$		0			0
$363$	−0.563016	−	0.132420i	−0.563016	−	0.132420i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.798017	−	0.602635i	$-0.794118\pi$
$367$		0			0		0.798017	+	0.602635i	$0.205882\pi$
$368$		0			0
$369$	0.0235979	+	0.510416i	0.0235979	+	0.510416i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$373$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$374$		−	1.92365i		−	1.92365i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.322039	+	0.831277i	0.322039	+	0.831277i	0.995734	+	0.0922684i	$0.0294118\pi$
$379$	0.322039	+	0.831277i	0.322039	+	0.831277i	−0.673696	+	0.739009i	$0.735294\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$383$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$384$	1.21146	+	0.406040i	1.21146	+	0.406040i
$385$		0			0
$386$	1.60263	+	0.798017i	1.60263	+	0.798017i
$387$	0.398152	+	1.18792i	0.398152	+	1.18792i
$388$	0.629488	−	0.0878098i	0.629488	−	0.0878098i
$389$		0			0		0.0922684	−	0.995734i	$-0.470588\pi$
$389$		0			0		−0.0922684	+	0.995734i	$0.529412\pi$
$390$		0			0
$391$		0			0
$392$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$393$	−0.0966148	−	0.339566i	−0.0966148	−	0.339566i
$394$		0			0
$395$		0			0
$396$	0.749354	−	0.140079i	0.749354	−	0.140079i
$397$		0			0		−0.932472	−	0.361242i	$-0.882353\pi$
$397$		0			0		0.932472	+	0.361242i	$0.117647\pi$
$398$		0			0
$399$		0			0
$400$	0.895163	−	0.445738i	0.895163	−	0.445738i
$401$	−0.0653133	−	0.0653133i	−0.0653133	−	0.0653133i	0.673696	−	0.739009i	$-0.264706\pi$
$401$	−0.0653133	−	0.0653133i	−0.0653133	−	0.0653133i	−0.739009	+	0.673696i	$0.764706\pi$
$402$	1.32445	−	1.45285i	1.32445	−	1.45285i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.823693	+	1.86549i	0.823693	+	1.86549i
$409$	−0.469302	+	0.757949i	−0.469302	+	0.757949i	−0.995734	−	0.0922684i	$-0.970588\pi$
$409$	−0.469302	+	0.757949i	−0.469302	+	0.757949i	0.526432	+	0.850217i	$0.323529\pi$
$410$		0			0
$411$	−0.176521	−	1.26544i	−0.176521	−	1.26544i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.233520	+	0.0325747i	0.233520	+	0.0325747i
$418$	0.441046	+	2.35939i	0.441046	+	2.35939i
$419$	0.887674	+	0.0822551i	0.887674	+	0.0822551i	0.526432	−	0.850217i	$-0.323529\pi$
$419$	0.887674	+	0.0822551i	0.887674	+	0.0822551i	0.361242	+	0.932472i	$0.382353\pi$
$420$		0			0
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	0.942485	−	0.469302i	0.942485	−	0.469302i
$423$		0			0
$424$		0			0
$425$	1.48826	+	0.576554i	1.48826	+	0.576554i
$426$		0			0
$427$		0			0
$428$	1.95756	−	0.181395i	1.95756	−	0.181395i
$429$		0			0
$430$		0			0
$431$		0			0		0.973438	−	0.228951i	$-0.0735294\pi$
$431$		0			0		−0.973438	+	0.228951i	$0.926471\pi$
$432$	0.387379	−	0.265360i	0.387379	−	0.265360i
$433$	−0.165190	+	1.78269i	−0.165190	+	1.78269i	0.361242	+	0.932472i	$0.382353\pi$
$433$	−0.165190	+	1.78269i	−0.165190	+	1.78269i	−0.526432	+	0.850217i	$0.676471\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.875259	+	0.293357i	0.875259	+	0.293357i
$439$		0			0		0.798017	−	0.602635i	$-0.205882\pi$
$439$		0			0		−0.798017	+	0.602635i	$0.794118\pi$
$440$		0			0
$441$	0.228486	−	0.589790i	0.228486	−	0.589790i
$442$		0			0
$443$	−0.646741	−	1.66943i	−0.646741	−	1.66943i	−0.739009	−	0.673696i	$-0.764706\pi$
$443$	−0.646741	−	1.66943i	−0.646741	−	1.66943i	0.0922684	−	0.995734i	$-0.470588\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	0.739009	+	0.673696i	$0.235294\pi$
$449$	−0.243964	+	0.857445i	−0.243964	+	0.857445i	−0.982973	+	0.183750i	$0.941176\pi$
$450$	−0.116222	+	0.621731i	−0.116222	+	0.621731i
$451$	0.309423	−	0.923193i	0.309423	−	0.923193i
$452$	1.29371	−	1.29371i	1.29371	−	1.29371i
$453$		0			0
$454$	−0.802895	+	1.44147i	−0.802895	+	1.44147i
$455$		0			0
$456$	−1.43798	−	2.09919i	−1.43798	−	2.09919i
$457$	−0.800095	+	1.81204i	−0.800095	+	1.81204i	−0.273663	+	0.961826i	$0.588235\pi$
$457$	−0.800095	+	1.81204i	−0.800095	+	1.81204i	−0.526432	+	0.850217i	$0.676471\pi$
$458$		0			0
$459$	0.729514	+	0.171580i	0.729514	+	0.171580i
$460$		0			0
$461$		0			0		0.850217	−	0.526432i	$-0.176471\pi$
$461$		0			0		−0.850217	+	0.526432i	$0.823529\pi$
$462$		0			0
$463$		0			0		0.138156	−	0.990410i	$-0.455882\pi$
$463$		0			0		−0.138156	+	0.990410i	$0.544118\pi$
$464$		0			0
$465$		0			0
$466$	0.434164	+	1.84595i	0.434164	+	1.84595i
$467$	−0.172075	−	1.85699i	−0.172075	−	1.85699i	−0.445738	−	0.895163i	$-0.647059\pi$
$467$	−0.172075	−	1.85699i	−0.172075	−	1.85699i	0.273663	−	0.961826i	$-0.411765\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.14558	−	1.25664i	−1.14558	−	1.25664i
$473$	0.110259	−	2.38488i	0.110259	−	2.38488i
$474$		0			0
$475$	−1.95756	−	0.365931i	−1.95756	−	0.365931i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.526432	−	0.850217i	$-0.676471\pi$
$479$		0			0		0.526432	+	0.850217i	$0.323529\pi$
$480$		0			0
$481$		0			0
$482$	−0.602635	+	0.201983i	−0.602635	+	0.201983i
$483$		0			0
$484$	−0.444966	−	0.0831786i	−0.444966	−	0.0831786i
$485$		0			0
$486$	−0.0510389	+	1.10395i	−0.0510389	+	1.10395i
$487$		0			0		−0.673696	−	0.739009i	$-0.735294\pi$
$487$		0			0		0.673696	+	0.739009i	$0.264706\pi$
$488$		0			0
$489$	−1.79056	−	1.63231i	−1.79056	−	1.63231i
$490$		0			0
$491$	−1.24376	−	1.49780i	−1.24376	−	1.49780i	−0.798017	−	0.602635i	$-0.794118\pi$
$491$	−1.24376	−	1.49780i	−1.24376	−	1.49780i	−0.445738	−	0.895163i	$-0.647059\pi$
$492$	0.0952371	+	1.02777i	0.0952371	+	1.02777i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.79242	+	1.10982i	−1.79242	+	1.10982i
$499$	1.37821	−	0.533922i	1.37821	−	0.533922i	0.445738	−	0.895163i	$-0.352941\pi$
$499$	1.37821	−	0.533922i	1.37821	−	0.533922i	0.932472	+	0.361242i	$0.117647\pi$
$500$		0			0
$501$		0			0
$502$	0.111609	−	0.252769i	0.111609	−	0.252769i
$503$		0			0		−0.565136	−	0.824997i	$-0.691176\pi$
$503$		0			0		0.565136	+	0.824997i	$0.308824\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.903466	−	0.903466i	0.903466	−	0.903466i
$508$		0			0
$509$		0			0		0.183750	−	0.982973i	$-0.441176\pi$
$509$		0			0		−0.183750	+	0.982973i	$0.558824\pi$
$510$		0			0
$511$		0			0
$512$	0.961826	+	0.273663i	0.961826	+	0.273663i
$513$	−0.934099	−	0.0431860i	−0.934099	−	0.0431860i
$514$	0.831277	−	1.66943i	0.831277	−	1.66943i
$515$		0			0
$516$	0.914260	+	2.35998i	0.914260	+	2.35998i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.765964	−	0.256725i	−0.765964	−	0.256725i	−0.0922684	−	0.995734i	$-0.529412\pi$
$521$	−0.765964	−	0.256725i	−0.765964	−	0.256725i	−0.673696	+	0.739009i	$0.735294\pi$
$522$		0			0
$523$	−1.32307	−	0.658809i	−1.32307	−	0.658809i	−0.361242	−	0.932472i	$-0.617647\pi$
$523$	−1.32307	−	0.658809i	−1.32307	−	0.658809i	−0.961826	+	0.273663i	$0.911765\pi$
$524$	−0.0878098	−	0.261989i	−0.0878098	−	0.261989i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.49906	−	0.352576i	1.49906	−	0.352576i
$529$	0.961826	−	0.273663i	0.961826	−	0.273663i
$530$		0			0
$531$	1.07094	−	0.0992370i	1.07094	−	0.0992370i
$532$		0			0
$533$		0			0
$534$	1.15949	+	0.449191i	1.15949	+	0.449191i
$535$		0			0
$536$	0.982973	−	1.18375i	0.982973	−	1.18375i
$537$	2.09258	−	1.04198i	2.09258	−	1.04198i
$538$		0			0
$539$	−0.811985	+	0.890705i	−0.811985	+	0.890705i
$540$		0			0
$541$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$541$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$542$		0			0
$543$		0			0
$544$	0.711414	+	1.42871i	0.711414	+	1.42871i
$545$		0			0
$546$		0			0
$547$	−1.86494			−1.86494			−0.932472	−	0.361242i	$-0.882353\pi$
$547$	−1.86494			−1.86494			−0.932472	+	0.361242i	$0.882353\pi$
$548$	−0.183750	−	0.982973i	−0.183750	−	0.982973i
$549$		0			0
$550$	0.634493	−	1.02474i	0.634493	−	1.02474i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.183750	+	0.0170269i	0.183750	+	0.0170269i
$557$		0			0		0.673696	−	0.739009i	$-0.264706\pi$
$557$		0			0		−0.673696	+	0.739009i	$0.735294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.02771	+	1.38901i	2.02771	+	1.38901i
$562$	−0.172075	−	0.0666624i	−0.172075	−	0.0666624i
$563$	−1.93247	+	0.361242i	−1.93247	+	0.361242i	−0.932472	+	0.361242i	$0.882353\pi$
$563$	−1.93247	+	0.361242i	−1.93247	+	0.361242i	−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	−0.368731	−	1.29596i	−0.368731	−	1.29596i
$567$		0			0
$568$		0			0
$569$	−1.64823	+	1.12907i	−1.64823	+	1.12907i	−0.798017	+	0.602635i	$0.794118\pi$
$569$	−1.64823	+	1.12907i	−1.64823	+	1.12907i	−0.850217	+	0.526432i	$0.823529\pi$
$570$		0			0
$571$	−1.11943	+	0.156154i	−1.11943	+	0.156154i	−0.673696	−	0.739009i	$-0.735294\pi$
$571$	−1.11943	+	0.156154i	−1.11943	+	0.156154i	−0.445738	+	0.895163i	$0.647059\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.504747	+	0.381167i	−0.504747	+	0.381167i
$577$	0.0127611	+	0.0914812i	0.0127611	+	0.0914812i	0.995734	−	0.0922684i	$-0.0294118\pi$
$577$	0.0127611	+	0.0914812i	0.0127611	+	0.0914812i	−0.982973	+	0.183750i	$0.941176\pi$
$578$	−0.558959	+	1.44284i	−0.558959	+	1.44284i
$579$	−1.99840	+	1.11310i	−1.99840	+	1.11310i
$580$		0			0
$581$		0			0
$582$	−0.361975	+	0.726944i	−0.361975	+	0.726944i
$583$		0			0
$584$	0.694903	+	0.197717i	0.694903	+	0.197717i
$585$		0			0
$586$		0			0
$587$	−0.100571	+	0.538007i	−0.100571	+	0.538007i	0.895163	+	0.445738i	$0.147059\pi$
$587$	−0.100571	+	0.538007i	−0.100571	+	0.538007i	−0.995734	+	0.0922684i	$0.970588\pi$
$588$	0.406040	−	1.21146i	0.406040	−	1.21146i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.258777	+	0.377767i	0.258777	+	0.377767i	0.932472	−	0.361242i	$-0.117647\pi$
$593$	0.258777	+	0.377767i	0.258777	+	0.377767i	−0.673696	+	0.739009i	$0.735294\pi$
$594$	0.228593	−	0.517714i	0.228593	−	0.517714i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.486604	−	0.873622i	$-0.661765\pi$
$599$		0			0		0.486604	+	0.873622i	$0.338235\pi$
$600$	−0.176521	+	1.26544i	−0.176521	+	1.26544i
$601$	−0.987432	−	0.549996i	−0.987432	−	0.549996i	−0.0922684	−	0.995734i	$-0.529412\pi$
$601$	−0.987432	−	0.549996i	−0.987432	−	0.549996i	−0.895163	+	0.445738i	$0.852941\pi$
$602$		0			0
$603$	0.222817	+	0.947359i	0.222817	+	0.947359i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.739009	−	0.673696i	$-0.764706\pi$
$607$		0			0		0.739009	+	0.673696i	$0.235294\pi$
$608$	−1.20013	−	1.58923i	−1.20013	−	1.58923i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.992305	−	0.185494i	−0.992305	−	0.185494i
$613$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$613$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$614$	−1.45890	+	0.488975i	−1.45890	+	0.488975i
$615$		0			0
$616$		0			0
$617$	1.01267	+	1.63552i	1.01267	+	1.63552i	0.739009	+	0.673696i	$0.235294\pi$
$617$	1.01267	+	1.63552i	1.01267	+	1.63552i	0.273663	+	0.961826i	$0.411765\pi$
$618$		0			0
$619$	−0.0875787	+	0.0293534i	−0.0875787	+	0.0293534i	−0.361242	−	0.932472i	$-0.617647\pi$
$619$	−0.0875787	+	0.0293534i	−0.0875787	+	0.0293534i	0.273663	+	0.961826i	$0.411765\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.602635	+	0.798017i	0.602635	+	0.798017i
$626$	−1.42160	−	1.29596i	−1.42160	−	1.29596i
$627$	−2.80548	−	1.23874i	−2.80548	−	1.23874i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.769334	−	0.638847i	$-0.220588\pi$
$631$		0			0		−0.769334	+	0.638847i	$0.779412\pi$
$632$		0			0
$633$	−0.185853	+	1.33234i	−0.185853	+	1.33234i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.07524	+	0.811985i	1.07524	+	0.811985i	0.982973	−	0.183750i	$-0.0588235\pi$
$641$	1.07524	+	0.811985i	1.07524	+	0.811985i	0.0922684	+	0.995734i	$0.470588\pi$
$642$	−1.22229	+	2.19443i	−1.22229	+	2.19443i
$643$	−0.0922684	−	1.99573i	−0.0922684	−	1.99573i	−0.0922684	−	0.995734i	$-0.529412\pi$
$643$	−0.0922684	−	1.99573i	−0.0922684	−	1.99573i		−	1.00000i	$-0.5\pi$
$644$		0			0
$645$		0			0
$646$	0.584039	−	3.12433i	0.584039	−	3.12433i
$647$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$647$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$648$			1.23244i			1.23244i
$649$	−1.97124	−	0.560867i	−1.97124	−	0.560867i
$650$		0			0
$651$		0			0
$652$	−1.45890	−	1.21146i	−1.45890	−	1.21146i
$653$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$653$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$654$		0			0
$655$		0			0
$656$	0.111609	+	0.800095i	0.111609	+	0.800095i
$657$	−0.364671	+	0.275387i	−0.364671	+	0.275387i
$658$		0			0
$659$	1.03397	−	0.456541i	1.03397	−	0.456541i	0.183750	−	0.982973i	$-0.441176\pi$
$659$	1.03397	−	0.456541i	1.03397	−	0.456541i	0.850217	+	0.526432i	$0.176471\pi$
$660$		0			0
$661$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$661$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$662$	−1.40065	+	0.195383i	−1.40065	+	0.195383i
$663$		0			0
$664$	−1.36124	+	0.932472i	−1.36124	+	0.932472i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.176521	−	0.212577i	0.176521	−	0.212577i	−0.673696	−	0.739009i	$-0.735294\pi$
$673$	0.176521	−	0.212577i	0.176521	−	0.212577i	0.850217	+	0.526432i	$0.176471\pi$
$674$	−0.646741	+	0.322039i	−0.646741	+	0.322039i
$675$	0.332023	+	0.332023i	0.332023	+	0.332023i
$676$	0.673696	−	0.739009i	0.673696	−	0.739009i
$677$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$677$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$678$	0.429543	+	2.29785i	0.429543	+	2.29785i
$679$		0			0
$680$		0			0
$681$	−0.939700	−	1.88717i	−0.939700	−	1.88717i
$682$		0			0
$683$	0.380338	−	0.614268i	0.380338	−	0.614268i	−0.602635	−	0.798017i	$-0.705882\pi$
$683$	0.380338	−	0.614268i	0.380338	−	0.614268i	0.982973	+	0.183750i	$0.0588235\pi$
$684$	1.25961			1.25961
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.800095	+	1.81204i	0.800095	+	1.81204i
$689$		0			0
$690$		0			0
$691$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.798017	−	0.602635i	$-0.205882\pi$
$691$	1.40065	+	0.195383i	1.40065	+	0.195383i	0.602635	+	0.798017i	$0.294118\pi$
$692$		0			0
$693$		0			0
$694$	−0.995734	+	1.09227i	−0.995734	+	1.09227i
$695$		0			0
$696$		0			0
$697$	−0.823693	+	0.991936i	−0.823693	+	0.991936i
$698$		0			0
$699$	−2.25930	−	0.875259i	−2.25930	−	0.875259i
$700$		0			0
$701$		0			0		0.602635	−	0.798017i	$-0.294118\pi$
$701$		0			0		−0.602635	+	0.798017i	$0.705882\pi$
$702$		0			0
$703$		0			0
$704$	1.15926	−	0.329838i	1.15926	−	0.329838i
$705$		0			0
$706$	0.932472	−	0.638758i	0.932472	−	0.638758i
$707$		0			0
$708$	2.15180	−	0.300163i	2.15180	−	0.300163i
$709$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$709$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$710$		0			0
$711$		0			0
$712$	0.922758	+	0.309277i	0.922758	+	0.309277i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.59837	−	0.890286i	1.59837	−	0.890286i
$717$		0			0
$718$		0			0
$719$		0			0		0.445738	−	0.895163i	$-0.352941\pi$
$719$		0			0		−0.445738	+	0.895163i	$0.647059\pi$
$720$		0			0
$721$		0			0
$722$			2.96595i			2.96595i
$723$	0.222236	−	0.781079i	0.222236	−	0.781079i
$724$		0			0
$725$		0			0
$726$	0.408976	−	0.408976i	0.408976	−	0.408976i
$727$		0			0		−0.0461835	−	0.998933i	$-0.514706\pi$
$727$		0			0		0.0461835	+	0.998933i	$0.485294\pi$
$728$		0			0
$729$	−0.143307	−	0.108221i	−0.143307	−	0.108221i
$730$		0			0
$731$	−1.27698	+	2.89208i	−1.27698	+	2.89208i
$732$		0			0
$733$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$733$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.256212	−	1.83673i	0.256212	−	1.83673i
$738$	−0.446387	−	0.248636i	−0.446387	−	0.248636i
$739$	−0.352279	+	0.292529i	−0.352279	+	0.292529i	−0.798017	−	0.602635i	$-0.794118\pi$
$739$	−0.352279	+	0.292529i	−0.352279	+	0.292529i	0.445738	+	0.895163i	$0.352941\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.914794	−	0.403921i	$-0.867647\pi$
$743$		0			0		0.914794	+	0.403921i	$0.132353\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0481981	−	1.04251i	0.0481981	−	1.04251i
$748$	1.63552	+	1.01267i	1.63552	+	1.01267i
$749$		0			0
$750$		0			0
$751$		0			0		0.948161	−	0.317791i	$-0.102941\pi$
$751$		0			0		−0.948161	+	0.317791i	$0.897059\pi$
$752$		0			0
$753$	0.185853	+	0.300163i	0.185853	+	0.300163i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$757$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$758$	−0.876298	−	0.163808i	−0.876298	−	0.163808i
$759$		0			0
$760$		0			0
$761$	−1.32445	−	1.45285i	−1.32445	−	1.45285i	−0.798017	−	0.602635i	$-0.794118\pi$
$761$	−1.32445	−	1.45285i	−1.32445	−	1.45285i	−0.526432	−	0.850217i	$-0.676471\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.982973	+	0.816250i	−0.982973	+	0.816250i
$769$	−1.70083	−	0.947359i	−1.70083	−	0.947359i	−0.961826	−	0.273663i	$-0.911765\pi$
$769$	−1.70083	−	0.947359i	−1.70083	−	0.947359i	−0.739009	−	0.673696i	$-0.764706\pi$
$770$		0			0
$771$	1.15949	+	2.08169i	1.15949	+	2.08169i
$772$	−1.52217	+	0.942485i	−1.52217	+	0.942485i
$773$		0			0		0.932472	−	0.361242i	$-0.117647\pi$
$773$		0			0		−0.932472	+	0.361242i	$0.882353\pi$
$774$	−1.21959	−	0.286846i	−1.21959	−	0.286846i
$775$		0			0
$776$	−0.256725	+	0.581427i	−0.256725	+	0.581427i
$777$		0			0
$778$		0			0
$779$	0.782845	−	1.40548i	0.782845	−	1.40548i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.273663	−	0.961826i	0.273663	−	0.961826i
$785$		0			0
$786$	0.339566	+	0.0966148i	0.339566	+	0.0966148i
$787$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.961826	−	0.273663i	$-0.0882353\pi$
$787$	1.89430	+	0.0875787i	1.89430	+	0.0875787i	0.932472	+	0.361242i	$0.117647\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.275387	+	0.710855i	−0.275387	+	0.710855i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.895163	−	0.445738i	$-0.852941\pi$
$797$		0			0		0.895163	+	0.445738i	$0.147059\pi$
$798$		0			0
$799$		0			0
$800$	−0.0922684	+	0.995734i	−0.0922684	+	0.995734i
$801$	−0.507832	+	0.347873i	−0.507832	+	0.347873i
$802$	0.0899135	−	0.0211475i	0.0899135	−	0.0211475i
$803$	0.837545	−	0.238302i	0.837545	−	0.238302i
$804$	0.538007	+	1.89090i	0.538007	+	1.89090i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.60617	+	1.10025i	1.60617	+	1.10025i	0.932472	+	0.361242i	$0.117647\pi$
$809$	1.60617	+	1.10025i	1.60617	+	1.10025i	0.673696	+	0.739009i	$0.264706\pi$
$810$		0			0
$811$	−0.942485	+	0.469302i	−0.942485	+	0.469302i	−0.850217	−	0.526432i	$-0.823529\pi$
$811$	−0.942485	+	0.469302i	−0.942485	+	0.469302i	−0.0922684	+	0.995734i	$0.529412\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−2.01969	−	0.281734i	−2.01969	−	0.281734i
$817$	0.903151	−	3.83996i	0.903151	−	3.83996i
$818$	−0.397365	−	0.798017i	−0.397365	−	0.798017i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	1.16883	+	0.516087i	1.16883	+	0.516087i
$823$		0			0		1.00000			$0$
$823$		0			0		−1.00000			$\pi$
$824$		0			0
$825$	0.622024	+	1.40875i	0.622024	+	1.40875i
$826$		0			0
$827$	−0.184956	+	0.786384i	−0.184956	+	0.786384i	0.798017	+	0.602635i	$0.205882\pi$
$827$	−0.184956	+	0.786384i	−0.184956	+	0.786384i	−0.982973	+	0.183750i	$0.941176\pi$
$828$		0			0
$829$		0			0		−0.183750	−	0.982973i	$-0.558824\pi$
$829$		0			0		0.183750	+	0.982973i	$0.441176\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.42871	−	0.711414i	1.42871	−	0.711414i
$834$	−0.150628	+	0.181395i	−0.150628	+	0.181395i
$835$		0			0
$836$	−2.23817	−	0.867072i	−2.23817	−	0.867072i
$837$		0			0
$838$	−0.537235	+	0.711414i	−0.537235	+	0.711414i
$839$		0			0		0.995734	−	0.0922684i	$-0.0294118\pi$
$839$		0			0		−0.995734	+	0.0922684i	$0.970588\pi$
$840$		0			0
$841$	−0.961826	+	0.273663i	−0.961826	+	0.273663i
$842$		0			0
$843$	0.194519	−	0.133249i	0.194519	−	0.133249i
$844$	−0.0971461	+	1.04837i	−0.0971461	+	1.04837i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.63231	+	0.547095i	1.63231	+	0.547095i
$850$	−1.27366	+	0.961826i	−1.27366	+	0.961826i
$851$		0			0
$852$		0			0
$853$		0			0		0.873622	−	0.486604i	$-0.161765\pi$
$853$		0			0		−0.873622	+	0.486604i	$0.838235\pi$
$854$		0			0
$855$		0			0
$856$	−0.876298	+	1.75984i	−0.876298	+	1.75984i
$857$	−1.53703	−	0.0710610i	−1.53703	−	0.0710610i	−0.739009	−	0.673696i	$-0.764706\pi$
$857$	−1.53703	−	0.0710610i	−1.53703	−	0.0710610i	−0.798017	+	0.602635i	$0.794118\pi$
$858$		0			0
$859$			1.86494i			1.86494i	0.361242	+	0.932472i	$0.382353\pi$
$859$			1.86494i			1.86494i	−0.361242	+	0.932472i	$0.617647\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$	0.0216855	+	0.469050i	0.0216855	+	0.469050i
$865$		0			0
$866$	−1.42871	−	1.07891i	−1.42871	−	1.07891i
$867$	−1.11728	−	1.63103i	−1.11728	−	1.63103i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.195618	−	0.351202i	−0.195618	−	0.351202i
$874$		0			0
$875$		0			0
$876$	−0.710182	+	0.589727i	−0.710182	+	0.589727i
$877$		0			0		−0.228951	−	0.973438i	$-0.573529\pi$
$877$		0			0		0.228951	+	0.973438i	$0.426471\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.32307	−	1.20614i	−1.32307	−	1.20614i	−0.961826	−	0.273663i	$-0.911765\pi$
$881$	−1.32307	−	1.20614i	−1.32307	−	1.20614i	−0.361242	−	0.932472i	$-0.617647\pi$
$882$	0.381167	+	0.504747i	0.381167	+	0.504747i
$883$	−0.124322	−	0.136374i	−0.124322	−	0.136374i	0.673696	−	0.739009i	$-0.264706\pi$
$883$	−0.124322	−	0.136374i	−0.124322	−	0.136374i	−0.798017	+	0.602635i	$0.794118\pi$
$884$		0			0
$885$		0			0
$886$	1.75984	+	0.328972i	1.75984	+	0.328972i
$887$		0			0		0.739009	−	0.673696i	$-0.235294\pi$
$887$		0			0		−0.739009	+	0.673696i	$0.764706\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.781976	+	1.26293i	0.781976	+	1.26293i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.600584	−	0.658809i	−0.600584	−	0.658809i
$899$		0			0
$900$	−0.467424	−	0.426113i	−0.467424	−	0.426113i
$901$		0			0
$902$	0.622024	+	0.749075i	0.622024	+	0.749075i
$903$		0			0
$904$	0.418885	+	1.78099i	0.418885	+	1.78099i
$905$		0			0
$906$		0			0
$907$	0.156154	−	1.11943i	0.156154	−	1.11943i	−0.739009	−	0.673696i	$-0.764706\pi$
$907$	0.156154	−	1.11943i	0.156154	−	1.11943i	0.895163	−	0.445738i	$-0.147059\pi$
$908$	−0.802895	−	1.44147i	−0.802895	−	1.44147i
$909$		0			0
$910$		0			0
$911$		0			0		−0.973438	−	0.228951i	$-0.926471\pi$
$911$		0			0		0.973438	+	0.228951i	$0.0735294\pi$
$912$	2.54177	−	0.117513i	2.54177	−	0.117513i
$913$	−0.803273	+	1.81924i	−0.803273	+	1.81924i
$914$	−1.11943	−	1.63417i	−1.11943	−	1.63417i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.529920	+	0.529920i	−0.529920	+	0.529920i
$919$		0			0		0.317791	−	0.948161i	$-0.397059\pi$
$919$		0			0		−0.317791	+	0.948161i	$0.602941\pi$
$920$		0			0
$921$	0.538007	−	1.89090i	0.538007	−	1.89090i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.694903	−	1.79375i	0.694903	−	1.79375i	0.0922684	−	0.995734i	$-0.470588\pi$
$929$	0.694903	−	1.79375i	0.694903	−	1.79375i	0.602635	−	0.798017i	$-0.294118\pi$
$930$		0			0
$931$	−1.58923	+	1.20013i	−1.58923	+	1.20013i
$932$	−1.79802	−	0.602635i	−1.79802	−	0.602635i
$933$		0			0
$934$	1.66943	+	0.831277i	1.66943	+	0.831277i
$935$		0			0
$936$		0			0
$937$	−0.124322	+	1.34164i	−0.124322	+	1.34164i	0.673696	+	0.739009i	$0.264706\pi$
$937$	−0.124322	+	1.34164i	−0.124322	+	1.34164i	−0.798017	+	0.602635i	$0.794118\pi$
$938$		0			0
$939$	2.39255	−	0.562723i	2.39255	−	0.562723i
$940$		0			0
$941$		0			0		−0.273663	−	0.961826i	$-0.588235\pi$
$941$		0			0		0.273663	+	0.961826i	$0.411765\pi$
$942$		0			0
$943$		0			0
$944$	1.67148	−	0.312454i	1.67148	−	0.312454i
$945$		0			0
$946$	1.96962	+	1.34922i	1.96962	+	1.34922i
$947$	−0.292529	+	0.352279i	−0.292529	+	0.352279i	−0.895163	−	0.445738i	$-0.852941\pi$
$947$	−0.292529	+	0.352279i	−0.292529	+	0.352279i	0.602635	+	0.798017i	$0.294118\pi$
$948$		0			0
$949$		0			0
$950$	1.34164	−	1.47171i	1.34164	−	1.47171i
$951$		0			0
$952$		0			0
$953$	1.73049	+	0.241393i	1.73049	+	0.241393i	0.932472	−	0.361242i	$-0.117647\pi$
$953$	1.73049	+	0.241393i	1.73049	+	0.241393i	0.798017	+	0.602635i	$0.205882\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.526432	−	0.850217i	0.526432	−	0.850217i
$962$		0			0
$963$	−0.554259	−	1.11310i	−0.554259	−	1.11310i
$964$	0.145517	−	0.618701i	0.145517	−	0.618701i
$965$		0			0
$966$		0			0
$967$		0			0		−0.995734	−	0.0922684i	$-0.970588\pi$
$967$		0			0		0.995734	+	0.0922684i	$0.0294118\pi$
$968$	0.304965	−	0.334530i	0.304965	−	0.334530i
$969$	2.87162	+	2.87162i	2.87162	+	2.87162i
$970$		0			0
$971$	−0.0590083	+	0.0710610i	−0.0590083	+	0.0710610i	−0.798017	−	0.602635i	$-0.794118\pi$
$971$	−0.0590083	+	0.0710610i	−0.0590083	+	0.0710610i	0.739009	+	0.673696i	$0.235294\pi$
$972$	−0.911733	−	0.624551i	−0.911733	−	0.624551i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.961826	−	0.273663i	$-0.0882353\pi$
$977$		0			0		−0.961826	+	0.273663i	$0.911765\pi$
$978$	2.33042	−	0.663063i	2.33042	−	0.663063i
$979$	1.14182	−	0.268554i	1.14182	−	0.268554i
$980$		0			0
$981$		0			0
$982$	1.92821	−	0.268973i	1.92821	−	0.268973i
$983$		0			0		−0.317791	−	0.948161i	$-0.602941\pi$
$983$		0			0		0.317791	+	0.948161i	$0.397059\pi$
$984$	−0.923965	−	0.460080i	−0.923965	−	0.460080i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.361242	−	0.932472i	$-0.617647\pi$
$991$		0			0		0.361242	+	0.932472i	$0.382353\pi$
$992$		0			0
$993$	0.805419	−	1.61750i	0.805419	−	1.61750i
$994$		0			0
$995$		0			0
$996$		−	2.10819i		−	2.10819i
$997$		0			0		0.273663	−	0.961826i	$-0.411765\pi$
$997$		0			0		−0.273663	+	0.961826i	$0.588235\pi$
$998$	−0.271585	+	1.45285i	−0.271585	+	1.45285i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1096.1.z.a.443.1	✓	32
8.3	odd	2	CM	1096.1.z.a.443.1	✓	32
137.30	even	68	inner	1096.1.z.a.715.1	yes	32
1096.715	odd	68	inner	1096.1.z.a.715.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1096.1.z.a.443.1	✓	32	1.1	even	1	trivial
1096.1.z.a.443.1	✓	32	8.3	odd	2	CM
1096.1.z.a.715.1	yes	32	137.30	even	68	inner
1096.1.z.a.715.1	yes	32	1096.715	odd	68	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1096 = 2^{3} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1096.z (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.516087 - 1.16883i) q^{3} +(-0.445738 - 0.895163i) q^{4} +(1.26544 + 0.176521i) q^{6} +(0.995734 + 0.0922684i) q^{8} +(-0.426113 + 0.467424i) q^{9} +O(q^{10})\)	\(q+(-0.526432 + 0.850217i) q^{2} +(-0.516087 - 1.16883i) q^{3} +(-0.445738 - 0.895163i) q^{4} +(1.26544 + 0.176521i) q^{6} +(0.995734 + 0.0922684i) q^{8} +(-0.426113 + 0.467424i) q^{9} +(1.07891 - 0.537235i) q^{11} +(-0.816250 + 0.982973i) q^{12} +(-0.602635 + 0.798017i) q^{16} +(-1.58923 + 0.147263i) q^{17} +(-0.173092 - 0.608356i) q^{18} +(1.91545 - 0.544991i) q^{19} +(-0.111208 + 1.20013i) q^{22} +(-0.406040 - 1.21146i) q^{24} +(-0.895163 - 0.445738i) q^{25} +(-0.445210 - 0.149219i) q^{27} +(-0.361242 - 0.932472i) q^{32} +(-1.18475 - 0.983802i) q^{33} +(0.711414 - 1.42871i) q^{34} +(0.608356 + 0.173092i) q^{36} +(-0.544991 + 1.91545i) q^{38} +(0.571231 - 0.571231i) q^{41} +(0.963876 - 1.73049i) q^{43} +(-0.961826 - 0.726337i) q^{44} +(1.24376 + 0.292529i) q^{48} +(-0.932472 + 0.361242i) q^{49} +(0.850217 - 0.526432i) q^{50} +(0.992305 + 1.78153i) q^{51} +(0.361242 - 0.299971i) q^{54} +(-1.62554 - 1.95756i) q^{57} +(-1.25664 - 1.14558i) q^{59} +(0.982973 + 0.183750i) q^{64} +(1.46013 - 0.489388i) q^{66} +(0.869557 - 1.26940i) q^{67} +(0.840204 + 1.35698i) q^{68} +(-0.467424 + 0.426113i) q^{72} +(0.710182 + 0.132756i) q^{73} +(-0.0590083 + 1.27633i) q^{75} +(-1.34164 - 1.47171i) q^{76} +(0.113716 + 1.22719i) q^{81} +(0.184956 + 0.786384i) q^{82} +(-1.26940 + 1.05409i) q^{83} +(0.963876 + 1.73049i) q^{86} +(1.12388 - 0.435393i) q^{88} +(0.947359 + 0.222817i) q^{89} +(-0.903466 + 0.903466i) q^{96} +(-0.201983 + 0.602635i) q^{97} +(0.183750 - 0.982973i) q^{98} +(-0.208623 + 0.733232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6}+O(q^{10}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6	\( 32 q - 2 q^{3} + 2 q^{4} - 2 q^{6} - 32 q^{12} - 2 q^{16} - 2 q^{18} - 4 q^{22} + 2 q^{24} + 4 q^{33} - 2 q^{41} + 2 q^{43} - 2 q^{48} + 2 q^{49} + 2 q^{50} - 4 q^{59} + 2 q^{64} - 4 q^{66} + 2 q^{67} + 2 q^{72} - 2 q^{75} - 2 q^{81} + 2 q^{82} - 2 q^{83} + 2 q^{86} + 4 q^{88} + 2 q^{89} - 2 q^{96} - 32 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 2 * q^4 - 2 * q^6 - 32 * q^12 - 2 * q^16 - 2 * q^18 - 4 * q^22 + 2 * q^24 + 4 * q^33 - 2 * q^41 + 2 * q^43 - 2 * q^48 + 2 * q^49 + 2 * q^50 - 4 * q^59 + 2 * q^64 - 4 * q^66 + 2 * q^67 + 2 * q^72 - 2 * q^75 - 2 * q^81 + 2 * q^82 - 2 * q^83 + 2 * q^86 + 4 * q^88 + 2 * q^89 - 2 * q^96 - 32 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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